Miscellaneous 5-limit temperaments: Difference between revisions

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 == Shibboleth ==
-: ''For extensions, see [[Gamelismic clan #Superkleismic]], [[Starling temperaments #Gilead]], and [[Sensamagic clan #Superthird]].''
+: ''For extensions, see [[Gamelismic clan #Superkleismic]] and [[Sensamagic clan #Superthird]].''
 [[Subgroup]]: 2.3.5
@@ Line 319: / Line 319: @@
 [[Badness]] (Sintel): 6.65
+== Octoid ==
+: ''For extensions, see [[Ragismic microtemperaments #Octoid]].''
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{monzo| -5 -32 24 }}
+{{Mapping|legend=1| 8 1 3 | 0 3 4 }}
+: Mapping generators: ~2125764/1953125, ~4374/3125
+[[Optimal tuning]]s:
+* [[WE]]: ~2125764/1953125 = 150.001{{c}}, ~4374/3125 = 584.027{{c}}
+* [[CWE]]: ~2125764/1953125 = 150.000{{c}}, ~4374/3125 = 584.025{{c}}
+{{Optimal ET sequence|legend=1| 8, 56bcc, 64c, 72, 152, 224, 376, 976 }}
+[[Badness]] (Sintel): 6.69
 == Kangaroo ==
@@ Line 512: / Line 530: @@
 Scales (Scala files): [[wizard22]]
+== Tridecatonic ==
+: ''For extensions, see [[Octagar temperaments #Tridecatonic]], [[Ragismic microtemperaments #Trideci]], and [[Varunismic temperaments #Bosonic]].''
+Tridecatonic tempers out the [[devil's tridecalimma]], the comma which associates the [[10/9]] minor tone with [[13edo|2\13]].
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{monzo| -11 26 -13 }}
+{{Mapping|legend=1| 13 0 -11 | 0 1 2 }}
+: mapping generators: ~531441/500000, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~531441/500000 = 92.3166{{c}}, ~3/2 = 701.2353{{c}}
+: [[error map]]: {{val| +0.116 -0.688 +0.737 }}
+* [[CWE]]: ~531441/500000 = 92.3077{{c}}, ~3/2 = 701.2353{{c}}
+: error map: {{val| 0.000 -0.797 +0.617 }}
+{{Optimal ET sequence|legend=1| 26, 39, 65, 286, 351, 416, 481, 546 }}
+[[Badness]] (Sintel): 10.3
 == Merman ==
@@ Line 529: / Line 569: @@
 [[Badness]] (Sintel): 10.6
+== Hendecatonic ==
+: ''For extensions, see [[Porwell temperaments #Hendecatonic]] and [[Marvel temperaments #Hendeca]].''
+The 5-limit version of hendecatonic simply equates a stack of eleven [[16/15]]'s with the [[octave]].
+[[Subgroup]]: 2.3.5
+[[Comma list]]: 8796093022208/8649755859375
+{{Mapping|legend=1| 11 0 43 | 0 1 -1 }}
+: Mapping generators: ~16/15, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~16/15 = 109.0904{{c}}, ~3/2 = 702.6861{{c}}
+: [[error map]]: {{val| -0.445 +0.286 +0.613 }}
+* [[CWE]]: ~16/15 = 109.0909{{c}}, ~3/2 = 702.9082{{c}}
+: error map: {{val| 0.000 +0.953 +1.687 }}
+{{Optimal ET sequence|legend=1| 22, 55, 77, 99, 869bcc, 968bcc, 1067bccc, 1166bccc }}
+[[Badness]] (Sintel): 10.7
 == Nusecond ==
@@ Line 626: / Line 688: @@
 == Leapday ==
-: ''For extensions, see [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]].''
+: ''For extensions, see [[Sengic temperaments #Leapday]] and [[Porwell temperaments #Polypyth]].''
 [[Subgroup]]: 2.3.5
@@ Line 794: / Line 856: @@
 [[Badness]] (Sintel): 17.0
+== Undeka ==
+: ''For extensions, see [[Keemic temperaments #Undeka]].''
+Undeka has a period of 1/11 octave, like [[#Hendecatonic|hendecatonic]], but this temperament equates a stack of eleven 6/5's and three [[octave]]s, so that three periods represent [[6/5]].
+[[Subgroup]]: 2.3.5
+[[Comma list]]: 48828125/45349632
+{{Mapping|legend=1| 11 0 8 | 0 1 1 }}
+: Mapping generators: ~648/625, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~648/625 = 109.1809{{c}}, ~3/2 = 704.4091{{c}}
+: [[error map]]: {{val| +0.990 +3.444 -7.468 }}
+* [[CWE]]: ~648/625 = 109.0909{{c}}, ~3/2 = 704.6983{{c}}
+: error map: {{val| 0.000 +2.743 -8.888 }}
+{{Optimal ET sequence|legend=1| 22, 77c, 99c }}
+[[Badness]] (Sintel): 17.1
 == Kumonga ==
@@ Line 1,197: / Line 1,281: @@
 [[Badness]] (Sintel): 52.3
+== Triskaidekic ==
+: ''For extensions, see [[Orwellismic temperaments #Triskaidekic]].''
+[[Subgroup]]: 2.3.5
+[[Comma list]]: 1220703125/1073741824
+{{Mapping|legend=1| 13 0 30 | 0 1 0 }}
+: Mapping generators: ~128/125, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~128/125 = 92.589{{c}}, ~3/2 = 698.263{{c}}
+: [[error map]]: {{val| +3.656 -0.036 -8.647 }}
+* [[CWE]]: ~128/125 = 92.308{{c}}, ~3/2 = 698.068{{c}}
+: error map: {{val| 0.000 -3.887 -17.083 }}
+{{Optimal ET sequence|legend=1| 13, 26, 91cc }}
+[[Badness]] (Sintel): 52.6
 == Satin ==
@@ Line 1,277: / Line 1,381: @@
 [[Badness]] (Sintel): 203
+== Elven ==
+: ''For extensions, see [[Sensibeta temperaments #Elven]].''
+Elven has a period of 1/11 octave, like [[#Hendecatonic|hendecatonic]], but this temperament equates a stack of eleven [[3125/2916]]'s with the octave.
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{monzo| -23 -66 55 }}
+{{Mapping|legend=1| 11 2 7 | 0 5 6 }}
+: mapping generators: ~3125/2916, ~{{monzo| 10 29 -24 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~3125/2916 = 109.0998{{c}}, ~{{monzo| 10 29 -24 }} = 336.8921{{c}}
+: [[error map]]: {{val| +0.097 +0.705 -1.263 }}
+* [[CWE]]: ~3125/2916 = 109.0909{{c}}, ~{{monzo| 10 29 -24 }} = 336.8814{{c}}
+: error map: {{val| 0.000 +0.634 -1.389 }}
+{{Optimal ET sequence|legend=1| 121, 253, 374, 627c }}
+[[Badness]] (Sintel): 429
 == References ==
 [[Category:Temperament collections]]